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Recommending a sequence of activities for an ongoing case requires that the recommendations conform to the underlying business process and meet the performance goal of either completion time or process outcome. Existing work on next activity prediction can predict the future activity but cannot provide guarantees of the prediction being conformant or meeting the goal. Hence, we propose a goal-oriented next best activity recommendation. Our proposed framework uses a deep learning model to predict the next best activity and an estimated value of a goal given the activity. A reinforcement learning method explores the sequence of activities based on the estimates likely to meet one or more goals. We further address a real-world problem of multiple goals by introducing an additional reward function to balance the outcome of a recommended activity and satisfy the goal. We demonstrate the effectiveness of the proposed method on four real-world datasets with different characteristics. The results show that the recommendations from our proposed approach outperform in goal satisfaction and conformance compared to the existing state-of-the-art next best activity recommendation techniques.